Upper bounds on absorption and scattering

TL;DR

This paper introduces a convex optimization framework to establish fundamental bounds on nanophotonic scattering and absorption, accommodating complex material properties and verifying tightness through canonical examples.

Contribution

The paper presents a novel, efficient convex optimization method for deriving fundamental bounds in nanophotonics, including anisotropic and inhomogeneous materials, with no dual gaps observed.

Findings

Derived bounds on scattering, absorption, and extinction cross sections.

Verified tightness of bounds using optimized nanoparticles and shells.

Established bounds for Purcell's factor and local field enhancement.

Abstract

A general framework for determining fundamental bounds in nanophotonics is introduced in this paper. The theory is based on convex optimization of dual problems constructed from operators generated by electromagnetic integral equations. The optimized variable is a contrast current defined within a prescribed region of a given material constitutive relations. Two power conservation constraints analogous to optical theorem are utilized to tighten the bounds and to prescribe either losses or material properties. Thanks to the utilization of matrix rank-1 updates, modal decompositions, and model order reduction techniques, the optimization procedure is computationally efficient even for complicated scenarios. No dual gaps are observed. The method is well-suited to accommodate material anisotropy and inhomogeneity. To demonstrate the validity of the method, bounds on scattering, absorption, and extinction cross sections are derived first and evaluated for several canonical regions. The tightness of the bounds is verified by comparison to optimized spherical nanoparticles and shells. The next metric investigated is bi-directional scattering studied closely on a particular example of an electrically thin slab. Finally, the bounds are established for Purcell's factor and local field enhancement where a dimer is used as a practical example.